Thanks Capt Sensible - No, I don't have Norton loaded; tried it on one of the machines and it caused more problems than it cured.
Very nearly caught the culprit last night. I was tied up on the second machine when the 'sleeping' one started to chatter the H/D and then the usual six or seven attempts to read the floppy. Unfortunately I couldn't leave what I was doing and by the time I could, the thing had stopped. Anyway I shall catch the little swine one of these days

Will keep you all posted.